I imagine to be based in our house, though, and only sleep in the apartment once or twice a week.

I just want to throw this out - this makes me think you still do have a lot of work to do to decide if your marriage is a relationship you want to keep being in. Being out on dates a couple nights a week, is one thing, but sleeping over twice a week, well that can be a struggle for lots of couples, especially when both of them aren't happily poly and seeing people or good at keeping themselves entertained.

Don't know if you've already discussed with your husband that you are choosing to become that independent, but if not I'd make sure you do, and that he understands and agrees that he is going to be responsible to stay at home caring for the kids overnight without you so regularly. Make sure there is some benefit for him such as free time for himself, or some extra money he can spend as he likes on hobbies so it does not feel lopsided, if you haven't already worked that out.

I imagine that it would feel very threatening - my spouse getting an apartment and letting me know they were already planning on being gone up to twice a week - that on top of a newly open relationship would make me struggle with trusting that my partner wasn't planning on jumping ship any second. Just wonder if you've examined your motives closely, as it seems looking at an apartment before you have even found somebody you want to be in a relationship with seems hasty.

Then again maybe you are interested in casual hooking up? I hadn't gotten that impression from your original post but perhaps you are very eager to run with this and start making up for the years of missing sexual intimacy. Anyway, regardless, I just recommend thinking hard about how your actions look to your husband, what they mean for you, your marriage, and your family.

__________________
Happiness will never come to those who fail to appreciate what they already have.